Defining A Binary Relation On All Real Numbers

Question

Define a relation R on $\mathbb R$ (Set of all Real Numbers) as follows: For all real numbers $x$ and $y$, $x \mathrel{R} y$ if and only if $x = y$.

Since the set of all real numbers is infinite, how would I create set $R$ (A relation on the set of all real numbers) that satisfies the requirement above without listing out every single number? Thanks!

Answer 1

Try $R=\{(x,x) | x \in \mathbb{R}\}.$